reserve C for Category,
  C1,C2 for Subcategory of C;

theorem Th13:
  for C being Categorial Category, f being Morphism of C holds
  dom f = f`11 & cod f = f`12
proof
  let C be Categorial Category;
  let f be Morphism of C;
  reconsider A = dom f, B = cod f as Category by Th12;
  ex F being Functor of A,B st f = [[A,B], F] by Def6;
  hence thesis by MCART_1:85;
end;
